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Find the area of the triangle formed by ...

Find the area of the triangle formed by the tangents from the point (4, 3) to the circle `x^2+y^2=9` and the line joining their points of contact.

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(i) Tangents are drawn from the point (alpha, beta) to the parabola y^2 = 4ax . Show that the length of their chord of contact is : 1/|a| sqrt((beta^2 - 4aalpha) (beta^2 + 4a^2)) . Also show that the area of the triangle formed by the tangents from (alpha, beta) to parabola y^2 = 4ax and the chord of contact is (beta^2 - 4aalpha)^(3/2)/(2a) . (ii) Prove that the area of the triangle formed by the tangents at points t_1 and t_2 on the parabola y^2 = 4ax with the chord joining these two points is a^2/2 |t_1 - t_2|^3 .